OG - PS - #180

by **mww7786** Sun Jun 03, 2007 2:09 pm

Hello MGMAT,

I used the formula T = G1 + G2 + N -Both on this. Is there any way to get an overlapping sets over another approach to this one?

In a nation wide poll, N people were interviewed. if 25% of them answered "yes" to Question 1, and of those, 33% answered Yes to Question 2.
Which of the following expresssions would represent the number of people interviewed who did not answer "yes" to both?

a N/7

b. 6N/7

c. 5N/12

d 7N/12

e 11N/12

Overlapping set possible? or someotherway? besides trick formula?

by **GMAT 5/18** Tue Jun 05, 2007 3:27 pm

mww7786,

You can solve this using Overlapping Sets.

1Y 1N Total
2Y 1 X
2N X X
Total 3 12

Above, I have filed in an Overlapping Sets diagram, using 12 (N) as my "smart" number (something divisible by 25% and 33%). My columns are "Yes" to question 1, "No" to question 1, and total. My rows are "Yes" to question 2, "No" to question 2, and total.

Using the information in the question, I have filed in some of the boxes, with 3 and 1. The questions asks, how many did not answer yes to both. This number is represented by the X's in my diagram above, which total 11 (12-1).

The only answer choice that satisfies the numbers is e:

11(12)/12 = 11.

I hope this helps!

by **GMAT 5/18** Tue Jun 05, 2007 3:32 pm

Just realised that diagram didn't come out as I had planned. Let me try again.

1Y 1N Total
2Y 1 X
2N X X
Total 3 12

Not perfect....better though. :)

by **esledge** Tue Jun 05, 2007 5:41 pm

Thanks for your answer, GMAT 5/18!

I'll just add that I too would use the Double Set Matrix on this problem. In my opinion, it's better to draw the chart than to use the (T = G1 + G2 + N -Both) formula, even if they are mathematically the same--the visual nature of the chart makes it harder for you to confuse yourself. Furthermore, the Double Set Matrix technique will serve you well on just about every overlapping set problem on the GMAT. You shouldn't ever need any "trick formula."